Misconceptions about mathematics teaching

Recently I’ve attended a few e-learning seminars and workshops, where uninformed ignoramuses such as me get to sit at the feet, so to speak, of various international heavies. What’s been most fascinating is the audience discussion, and the chats I’ve had with other people afterwards. Maybe you know this already, but I’ve only just discovered it: other academics (not themselves mathematics teachers) are completely ignorant and misinformed about the nature both of mathematics, and of mathematics teaching. At a recent “discussion”, another participant – a professor of “design” – after giving a lengthy dissertation on why his subject wasn’t really suited to e-learning (too creative) managed to point out that “unlike, say, engineering mathematics”, the creative arts required an interaction that wasn’t supported by e-learning environments. And a further participant, a chemistry professor, told me afterwards that mathematics was clearly perfectly suited to online learning (unlike chemistry, which is clearly a much more subtle discipline!).

Now, I love tools and technology as much as anyone, and I do believe in the immense possibilities offered by online learning. But these two people – who I’m sure are representative of most – seemed to think that mathematics is somehow pedagogically “easier” than their own disciplines because a mathematics answer is either right or wrong, so it’s trivial to manage it online.

I find this attitude both insulting and patronizing.

Any of us who have helped struggling students learn proofs by induction, or how to solve an initial value problem (to give but two examples), will know that good mathematics teaching requires an immense flexibility of mind, a razor sharp eye, and incredible empathy. To enter into the mind of the student, to see the difficulties from “inside”, so to speak, requires a level of mental creativity that I believe is unmatched by any other discipline.

Now, I’m by far away from being the first to discuss creativity in mathematics; here’s another blog post which says pretty much the same thing. There’s a quote attributed to David Hilbert about a student: “He is all right. You know, for a mathematician he did not have enough imagination. But he has become a poet and now he is doing fine.” You can find this quote here.

What is so fascinating is that even among our peers (who aren’t mathematicians or mathematics educators), who we would expect to be enlightened, mathematics is still seen as a totally cut-and-dried discipline for which the teaching simply consists of providing students with recipes to solve different sorts of problems, and marking their efforts as either right or wrong.

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